I have successfully managed to boot up a E01 file using Virtualbox.
Regripper told me that the account had no password requirements.
However when trying to login I get the message "No internet connection, please enter your last used password" apparently it is using Microsoft account to validat each login.

Since there is no password I can't find the NTLM hash in the SAM-hive. There should be an old password located in any other hives? Does anyone know exactly where?

Sounds like a Windows Live account is being used.
I cannot remember of the top of my head where the hashes are for those accounts, but its not the default location.
Have a Google for Windows Live account hash location.

Regripper told me that the account had no password requirements.
However when trying to login I get the message "No internet connection, please enter your last used password" apparently it is using Microsoft account to validat each login.

Since there is no password I can't find the NTLM hash in the SAM-hive. There should be an old password located in any other hives? Does anyone know exactly where?

When the RegRipper samparse.pl plugin returns "Password Not Required", it's based on a flag check in the hive, and does NOT mean that the account doesn't have a password...it simply means that the account is not required to have a password. The distinction may seem subtle, but it's there.

Extract the System and SAM hives from the image, and use your favorite password extractor/cracker, like L0phtcrack or John the Ripper.